RF Pulse Design RF Pulses / Adiabatic Pulses

M229 Advanced Topics in MRI Kyung Sung, Ph.D.

2018.04.05

Class Business

• Office hours - Instructors: Fri 10-12pm

TAs: TBD - Emails beforehand would be helpful

• Homework 1 next week

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 ...

What is the Effective Magnetic Field (Beff)?

• Beff is the net sum of the magnetic fields in a system of spins

• Beff is the vector sum of the B0 and B1 fields at any given time

• At any given time, Beff is the only magnetic field that the spins “see”, and spins precess about Beff

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:

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

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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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SN82 DELAY LVOT

50 100 150 200 250

50

100

150

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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)

Thank You!

Kyung Sung, PhD ksung@mednet.ucla.edu http://kyungs.bol.ucla.edu

- 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.