RF Pulse Design RF Pulses / Adiabatic Pulses M229 Advanced Topics in MRI Kyung Sung, Ph.D. 2019.04.04 4/4/2019 - Ended at 11:45am - Needed to finish RF pulse review earlier (took an hour to finish)
RF Pulse Design RF Pulses / Adiabatic Pulses
M229 Advanced Topics in MRI Kyung Sung, Ph.D.
2019.04.04
4/4/2019
- Ended at 11:45am - Needed to finish RF pulse review earlier (took an
hour to finish)
Class Business
• Lecture #3 - Friday (4/5) - 10-12pm - No lecture on 4/9
• Homework 1 will be out on 4/5 (Fri) - Due on 4/26
• TA for HW1 is TBD
• Group email list / course website
Outline
• Review of RF pulses
• Adiabatic passage principle
• Adiabatic inversion
• Applications of adiabatic pulses
Review of RF Pulses
Notation and Conventions
• ω = carrier frequency
• ω0 = resonant frequency
• B1(t) = complex valued envelop function
~B = B0k +B1(t)[cos!ti� sin!tj]
RF Pulse - Excitation
t = ⌧pt = 0
t
carrier frequency ωenvelope B1(t)
~B = B0k +B1(t)[cos!ti� sin!tj]
Lab vs. Rotating Frame
X Y
Z
X’ Y’
Z=Z’
Laboratory Frame Rotating Frame
- The rotating frame simplifies the mathematics and permits more intuitive understanding.
Rotating Frame
~Mrot ⌘
2
4Mx0
My0
Mz0
3
5 ~Brot ⌘
2
4Bx0
By0
Bz0
3
5Mz0 ⌘Mz
Bz0 ⌘ Bz
Rotating Frame Definitions
~Mlab(t) = RZ(w0t) · ~Mrot(t)
~Blab(t) = RZ(w0t) · ~Brot(t)
d ~Mrot
dt= ~Mrot ⇥ � ~Beff
d ~M
dt= ~M ⇥ � ~B
Bloch Equation (Rotating Frame)
d ~Mrot
dt= ~Mrot ⇥ � ~Beff
~Beff = ~Brot +~wrot
�where
fictitiousfield
~!rot =
0
@00�!
1
A
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~Blab =
0
@B1(t) cos!0tB1(t) sin!0t
B0
1
A
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Bloch Equation (Rotating Frame)~Beff = ~Brot +
~wrot
�
~Brot =
0
@B1(t)B1(t)B0
1
A
Assume real-valued B1(t)
~Brot =
0
@B1(t)0B0
1
A ~Beff =
0
@B1(t)0
B0 � !�
1
A
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To the board ...
Bloch Equation with Gradient
d ~Mrot
dt= ~Mrot ⇥ � ~Beff
~Beff =
0
@B1(t)0
B0 � !�
1
A
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~Beff =
0
@B1(t)0
B0 � !� +Gzz
1
A
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Bloch Equation (at on-resonance)
d ~Mrot
dt= ~Mrot ⇥ � ~Beff
where
d ~M
dt=
0
@0 !(z) 0
�!(z) 0 !1(t)0 �!1(t) 0
1
A
To the board ...
B1 Variations
- In MRI, B1 field is not always uniform across the imaging volume
- B1 inhomogeneity can cause:
• Image shading
• Incomplete saturation (e.g. in fat suppression)
• Incomplete inversion (e.g. CSF suppression, myocardium suppression in cardiac scar imaging)
• Inaccurate/imprecise quantification in T1 mapping
B1 Variations
- It is highly desirable if we can excite tissue homogeneously and produce a uniform flip angle throughout
➔ Adiabatic Pulses!
“Adiabatic pulses are a special class of RF pulses that can excite, refocus or invert magnetization vectors uniformly, even in the presence of a spatially nonuniform B1 field.”
Adiabatic Passage Principle
Adiabatic Pulses- A special class of RF pulses that can achieve
uniform flip angle
- Flip angle is independent of the applied B1 field
- Slice profile of an adiabatic pulse is obtained using Bloch simulations
- Can be used for excitation, inversion and refocusing
✓ 6=Z T
0B1(⌧)d⌧
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Adiabatic vs. Non-Adiabatic Pulses
Adiabatic Pulses: Non-Adiabatic Pulses:
✓ =
Z T
0B1(⌧)d⌧
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✓ 6=Z T
0B1(⌧)d⌧
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- Amplitude and frequency/phase modulation
- Long duration (8-12 ms)
- Higher B1 amplitude (>12 µT)
- Generally NOT multi-purpose (inversion pulse cannot be used for refocusing, etc.)
- Amplitude modulation, constant carrier frequency (constant phase)
- Short duration (0.3 ms to 1 ms)
- Lower B1 amplitude
- Generally multi-purpose
Adiabatic Pulses
• Frequency modulated pulses:
• Or phase modulation:
envelop frequencysweep
Bloch Equation (at on-resonance)
where
d ~M
dt= ~M ⇥ � ~Beff
Magnetization Plot
To the board ...
a b d e a b d e
Adiabatic Excitation
▪ At the end of the pulse, all the magnetization is in the transverse plane ! so we have adiabatic excitation!
▪ This is also called an adiabatic half passage (AHP)
A(t)
tω1(t)
t
AHP
ω0
Adiabatic Inversion
- An adiabatic inversion requires an adiabatic full passage (AFP) pulse:
A(t)
t
ω1(t)
t
AFP
ω0
Adiabatic InversionA(t)
t
ω1(t)
t
AFP
ω0
Adiabatic Inversion
- General equation for an adiabatic pulse:
- Many different types of adiabatic pulses can be designed by choosing different amplitude and frequency modulation functions
- The most famous one is…
The Hyperbolic Secant Inversion Pulse!
Design of Adiabatic Inversion
Hyperbolic Secant Pulse Equations
where
A0: peak amplitude (µT) β: frequency modulation parameter (rad/s) µ: phase modulation parameter (dimensionless)
A(t) = A0sech(�t)<latexit sha1_base64="cIqgflqzrKDOntDz4yKwYUgvp94=">AAACC3icdVDJSgNBEO1xjXEb9eilSRCSS5gRQXMQEr14jGAWSELo6VSSJj0L3TViGHL34q948aCIV3/Am39jZxFcHxQ83qvqrnpeJIVGx3m3FhaXlldWU2vp9Y3NrW17Z7emw1hxqPJQhqrhMQ1SBFBFgRIakQLmexLq3vB84tevQWkRBlc4iqDts34geoIzNFLHzpRzmKentNxxaAvhxjyRaOCDMc21PEBGMd+xs06hWHQM6G/iFpwpsmSOSsd+a3VDHvsQIJdM66brRNhOmELBJYzTrVhDxPiQ9aFpaMB80O1kesuYHhilS3uhMhUgnapfJxLmaz3yPdPpMxzon95E/Mtrxtg7aSciiGKEgM8+6sWSYkgnwdCuUMBRjgxhXAmzK+UDphhHE1/ahPB5Kf2f1A4LrlNwL4+ypbN5HCmyTzIkR1xyTErkglRIlXByS+7JI3my7qwH69l6mbUuWPOZPfIN1usHJJ6ZPg==</latexit><latexit sha1_base64="cIqgflqzrKDOntDz4yKwYUgvp94=">AAACC3icdVDJSgNBEO1xjXEb9eilSRCSS5gRQXMQEr14jGAWSELo6VSSJj0L3TViGHL34q948aCIV3/Am39jZxFcHxQ83qvqrnpeJIVGx3m3FhaXlldWU2vp9Y3NrW17Z7emw1hxqPJQhqrhMQ1SBFBFgRIakQLmexLq3vB84tevQWkRBlc4iqDts34geoIzNFLHzpRzmKentNxxaAvhxjyRaOCDMc21PEBGMd+xs06hWHQM6G/iFpwpsmSOSsd+a3VDHvsQIJdM66brRNhOmELBJYzTrVhDxPiQ9aFpaMB80O1kesuYHhilS3uhMhUgnapfJxLmaz3yPdPpMxzon95E/Mtrxtg7aSciiGKEgM8+6sWSYkgnwdCuUMBRjgxhXAmzK+UDphhHE1/ahPB5Kf2f1A4LrlNwL4+ypbN5HCmyTzIkR1xyTErkglRIlXByS+7JI3my7qwH69l6mbUuWPOZPfIN1usHJJ6ZPg==</latexit><latexit sha1_base64="cIqgflqzrKDOntDz4yKwYUgvp94=">AAACC3icdVDJSgNBEO1xjXEb9eilSRCSS5gRQXMQEr14jGAWSELo6VSSJj0L3TViGHL34q948aCIV3/Am39jZxFcHxQ83qvqrnpeJIVGx3m3FhaXlldWU2vp9Y3NrW17Z7emw1hxqPJQhqrhMQ1SBFBFgRIakQLmexLq3vB84tevQWkRBlc4iqDts34geoIzNFLHzpRzmKentNxxaAvhxjyRaOCDMc21PEBGMd+xs06hWHQM6G/iFpwpsmSOSsd+a3VDHvsQIJdM66brRNhOmELBJYzTrVhDxPiQ9aFpaMB80O1kesuYHhilS3uhMhUgnapfJxLmaz3yPdPpMxzon95E/Mtrxtg7aSciiGKEgM8+6sWSYkgnwdCuUMBRjgxhXAmzK+UDphhHE1/ahPB5Kf2f1A4LrlNwL4+ypbN5HCmyTzIkR1xyTErkglRIlXByS+7JI3my7qwH69l6mbUuWPOZPfIN1usHJJ6ZPg==</latexit><latexit sha1_base64="cIqgflqzrKDOntDz4yKwYUgvp94=">AAACC3icdVDJSgNBEO1xjXEb9eilSRCSS5gRQXMQEr14jGAWSELo6VSSJj0L3TViGHL34q948aCIV3/Am39jZxFcHxQ83qvqrnpeJIVGx3m3FhaXlldWU2vp9Y3NrW17Z7emw1hxqPJQhqrhMQ1SBFBFgRIakQLmexLq3vB84tevQWkRBlc4iqDts34geoIzNFLHzpRzmKentNxxaAvhxjyRaOCDMc21PEBGMd+xs06hWHQM6G/iFpwpsmSOSsd+a3VDHvsQIJdM66brRNhOmELBJYzTrVhDxPiQ9aFpaMB80O1kesuYHhilS3uhMhUgnapfJxLmaz3yPdPpMxzon95E/Mtrxtg7aSciiGKEgM8+6sWSYkgnwdCuUMBRjgxhXAmzK+UDphhHE1/ahPB5Kf2f1A4LrlNwL4+ypbN5HCmyTzIkR1xyTErkglRIlXByS+7JI3my7qwH69l6mbUuWPOZPfIN1usHJJ6ZPg==</latexit>
!1(t) = �µ�tanh(�t)<latexit sha1_base64="Cu2RA90Rx+aoCL5n/ZrFQys8PAs=">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</latexit><latexit sha1_base64="Cu2RA90Rx+aoCL5n/ZrFQys8PAs=">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</latexit><latexit sha1_base64="Cu2RA90Rx+aoCL5n/ZrFQys8PAs=">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</latexit><latexit sha1_base64="Cu2RA90Rx+aoCL5n/ZrFQys8PAs=">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</latexit>
Handbook of MRI Pulse Sequences, Ch 6.2, pp 194-195
Amplitude Modulation, A(t) Frequency Modulation, ω1(t)
Pulse Parameters: A0 = 12 µT µ = 5 β = 672 rad/s Duration = 10.24 ms
Hyperbolic Secant Pulse Example
A(t)
t
ω1(t)
t
General Adiabatic Full Passage pulse
ω0
Hyperbolic Secant Pulse
Comparing Hyperbolic Secant with an AFP Example
Amplitude Modulation, A(t) Frequency Modulation, ω1(t)
Some Examples of Other Adiabatic Inversion Pulses
Pulse Name A(t) ω1(t)
Tannus et al., “Adiabatic Pulses”, NMR in Biomedicine, vol. 10, p423
Some Examples of Other Adiabatic Inversion Pulses
Pulse Name A(t) ω1(t)
Tannus et al., “Adiabatic Pulses”, NMR in Biomedicine, vol. 10, p423
The shape of the inversion profile depends on the choice A(t) and ω1(t)!
What Will Inversion Profile Look Like?
Hyp
erbo
lic S
ecan
t P
ulse
Amplitude Modulation, A(t) Frequency Modulation, ω1(t)
Inversion Profile
Inversion Profiles- The inversion profile typically calculated using
Bloch simulation of the RF pulse (will be covered later) shows us the inversion efficiency and RF bandwidth
- The inversion efficiency depends strongly on the B1 amplitude (as well as pulse duration, T1, T2 and pulse shape)
- For the hyperbolic secant pulse,
RF spectral bandwidth = µβ
B1max >> (!√")/# (B1 threshold for adiabaticity)
Original Pulse (100%) B1max = 12 µT
75% Attenuated Pulse B1max = 9 µT
Hyperbolic Secant: Adiabatic Property
Original Pulse (100%) B1max = 12 µT
Hyperbolic Secant: Adiabatic Property
60% Attenuated Pulse B1max = 7.2 µT
B1 Threshold ≈ 6 µT
Original Pulse (100%) B1 = 12 µT
125% Amplified Pulse B1 = 15 µT
150% Amplified Pulse B1 = 18 µT
Comments
• Many envelope/modulation functions work
• If a range of adiabaticity is required, optimization can help reduce pulse length
• Hyperbolic Sech needs to be truncated, which can affect the overall performance
Applications of Adiabatic Pulses
Adiabatic Pulses
- Fat suppression (STIR)
- CSF suppression (FLAIR)
- Myocardium suppression in cardiac scar imaging (LGE)
- Black blood cardiac imaging (DIR TSE)
- T1 Mapping
Late Gadolinium Enhancement (LGE)
- Gold standard for detection of scar/myocardial fibrosis
- Spoiled gradient echo (SPGR) sequence with an inversion pulse (inversion recovery SPGR)
• Inversion pulse is usually hyperbolic secant pulse
• Healthy myocardium is nulled with the inversion pulse
• Scar tissue (which has shorter T1 than healthy tissue) appear bright
▪ The conventional LGE sequence uses an RF-spoiled gradient echo (FLASH) readout with an inversion recovery (IR) pulse as a preparation pulse
▪ The readout is acquired at a time after inversion at which the healthy myocardium signal reaches zero
Inversion recovery curves of postcontrast scar (white) and myocardium (red)
Myocardium signal nullified
Hyper-enhanced scar region
Nullified signal from healthy myocardium
Clinical ExampleSN135 Delayed SA
50 100 150 200 250
20
40
60
80
100
120
140
160
180
SN121 Delayed HLA
50 100 150 200 250
20
40
60
80
100
120
140
160
180SN100 DELAY SA
50 100 150 200 250
50
100
150
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250
SN82 DELAY LVOT
50 100 150 200 250
50
100
150
200
250
Patient with healthy myocardium
Patient with scar tissue
Clinical ExampleLate Gadolinium Enhancement (LGE) in patients with implantable cardiac devices
▪ Presence of an implantable cardiac device in the patients produces an interesting off-resonance artifact
ICD
Hyper-intensity Artifacts
SN57 tfl25 t1 Delayed HLA SN47 tfl25 t1 Delayed HLA
ICD
Conventional IR LGE Image
Conventional IR LGE Image
Hyper-intensity artifact
Cause of Artifact
Longitudinal magnetization produced by conventional IR pulse
BW = 1.1 kHz
Solution: Increase Bandwidth of Inversion Pulse
Mz
Frequency (Hz)
Longitudinal magnetization produced by conventional IR pulse
BW = 1.1 kHz
Longitudinal magnetization produced by wideband IR pulse
BW = 3.8 kHz
SN57 tfl25 t1 Delayed HLA SN47 tfl25 t1 Delayed HLA
ICD ICD
Conventional IRLGE Image
Conventional IR LGE Image
Wideband IRLGE Image
Hyper-intensity artifact Hyper-intensity artifact correctedNo artifact (no ICD)
- Further reading • Read "Adiabatic Refocusing Pulses" p.200-212 • Tannus et al., “Adiabatic Pulses”, NMR in
Biomedicine, Vol. 10, 423-434 (1997)
- Acknowledgments • John Pauly’s EE469b (RF Pulse Design for MRI) • Shams Rashid, Ph.D.
Thank You!
Kyung Sung, PhD [email protected]
https://mrrl.ucla.edu/sunglab/