RF Pulse Design in Practice

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RF Pulse Design in Practice
Charles H. Cunningham, Ph.D. Magnetic
Resonance Systems Research Lab Stanford University
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Outline

• The role of RF pulses in pulse sequences
• Hard pulses
• Composite pulses
• Slice-selection
• SLR pulses for large tip angles
• the VERSE algorithm
• Non-linear phase pulses
• Adiabatic pulses
• Spectral-spatial pulses

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The role of RF pulses

• Excitation
• Spatial localization
• Contrast manipulation
• Refocusing

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Magnetization
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Excitation
During RF pulse
Before RF pulse
After
z
z
z
M
longitudinal magnetization
90o
y
y
y
transverse magnetization
x
x
rf pulse
x
Radio emission
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Hard Pulses
200 us
z
M
y
x
B1
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Imperfections
z
M
y
x
B1
RF phase inhomogeneity
RF amplitude inhomogeneity
Main field Inhomogeneity
z
z
z
DBo
B1
B1
y
y
y
-DBo
x
x
x
B1
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Composite pulses
90x
180y
90x
M.H. Levitt. Composite pulses. Progress in NMR
Spectroscopy 18 p.61 (1986)
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Selective Excitation
Radio wave emission
RF pulse
Cross-sectional image
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Breakdown of the small-tip approximation
RF pulse
30 degrees
90 degrees
180 degrees
Mxy
Mxy
Mxy
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Need for large tip-angle pulses

• 90-degree excitation maximum signal
• Saturation (90)
• Inversion (180)
• Spin-echo refocusing (180)

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Digitized waveform sequence of rotations
1 2 3 4
Rtotal RNR3R2R1
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Large-tip excitation a non-linear process

• computing the excitation profile of any
• RF pulse is trivial just multiply rotation
• matrices.
• deriving an RF pulse that gives a desired
• excitation profile much harder.

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Shinnar-Le Roux Transform

• Enables the design of large tip-angle RF pulses
• Pauly J, et al. IEEE T Med Imaging 10(1)53-65
  1991

SLR
FT
RFi
Ai,Bi
Mx,y
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The VERSE algorithm
max B1
VERSE
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VERSE rotation about the same axis
After VERSE
Before VERSE
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VERSE enables RF on gradient ramps
200 us
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Time-bandwidth product
TB5.0
TB10
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Nonlinear-phase RF pulses
RF pulse
Profile
RF pulse
Profile
Profile
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Hyperbolic secant pulse
8 ms
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Adiabatic Excitation Spin Locking
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Chemical shift mis-registration
frequency
water resonance
position
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Spatial vs. spectral profile for conventional
pulse

• Translation of slice as function of position
• Wide bandwidth at a given position

position mm
resonant frequency Hz
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Spectral-Spatial RF Pulse
7.2ms duration 1.2ms subpulses
Oscillating gradient 4G/cm
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Spatial vs. spectral profile for spectral-spatial
pulse

• Spatial profile almost independent of frequency
• Narrow spectral bandwidth (200Hz)

position mm
resonant frequency Hz
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Source of bipolar sidelobes

• Interference between excitations from positive
  and negative gradient lobes

position mm
position mm
position mm
resonant frequency Hz
resonant frequency Hz
resonant frequency Hz
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Spectral-Spatial Pulse in Excitation k-space
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Dual-band, dual-shim pulse for bilateral breast
MRI
RF
Volume excitation in both breasts
G
shim
Independent control over shims for each breast
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Spectral-spatial 3 T prostate spectroscopic
imaging

• Designed to be short, yet robust
• Body coil transmit
• 140 Hz passband for Cho, Cr, Cit
• /- 35 Hz tolerance in stopband
• 10-5 suppression of lipids
• partial suppression of water (10-2)

Schricker MRM 2002
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Summary

• The role of RF pulses in pulse sequences
• Hard pulses
• Composite pulses
• Slice-selection
• SLR pulses for large tip angles
• the VERSE algorithm
• Non-linear phase pulses
• Adiabatic pulses
• Spectral-spatial pulses

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Spins with different resonances
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G(t) and spins with different resonances

• With time-varying gradient, gradient center moves
  around
• Excitation with time-varying gradients is
  inherently sensitive
• to off-resonance effects.

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Spectral k-space

• translation along kw during RF pulse
• constant rate, cant be controlled

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Spectral-Spatial Pulse How It Works
Set envelope and tau to exclude unwanted
frequencies.
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Dualband Spectral-Spatial for Prostate
Spectroscopy
A. Schricker et al. MRM 461079-1087 2001
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Design Example Dualband Spectral-Spatial for 3T

• Pulse length 30ms
• Maximum B1 0.15G
• Spectral profile 2x 1.5T but with sharper
  transition
• between water (attenuated) band and
  metabolites.
• Spatial profile as good as 1.5T pulse.

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Design Example Dualband Spectral-Spatial for 3T
Step 1 choose number of gradient sublobes 30
consider location of spectral sidelobes
(1 kHz) Step 2 design spectral beta-polynomial
FT
Step 3 introduce nonlinear phase in spectral
dimension
FT
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Design Example Dualband Spectral-Spatial for 3T
Step 4 design gradient sublobe.
consider maximum B1, minimum spatial width
Step 5 design spatial beta-polynomial.
consider spatial profile, maximum B1
Step 6 apply 2D inverse SLR transform to compute
RF
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Dualband spectral-spatial pulse for 3T
RF and gradient waveforms
Spectral and spatial profiles
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Summary

• Excitation k-space a useful concept for
  multidimensional
• pulses
• Large tip-angle excitation is a nonlinear
  process
• Shinnar Le-Roux Transform RFi Ai, Bi
• Nonlinear phase very selective saturation
  pulses
• Adiabatic pulses frequency sweep, spin locking
• Spectral-spatial pulses spatially selective,
  only spins
• with certain frequencies

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The Rotating Frame
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RF Pulse Design Tradeoffs and Constraints

• Constraints
• Peak RF amplitude
• Patient heating (SAR)
• Performance Parameters
• Bandwidth minimum slice thickness / chemical
  shift
• Duration
• Selectivity

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Proof of the Adiabatic Theorem
Frame rotating _at_ wo
Frame rotating _at_ wo - w
Insensitive to B1 inhomogeneity
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Root flipping to reduce peak B1
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Adiabatic Behavior of Non-Linear Phase Pulses