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G16.4427 Practical MRI 1

Pulse Design for Parallel MR Transmission. Outline. K-space analysis of small tip-angle excitation. RF shimming and Parallel MR Transmission. B. 1. mapping. Accelerated MR excitations. Homogeneity and SAR minimization.

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G16.4427 Practical MRI 1






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Slide1

G16.4427 Practical MRI 1

Pulse Design for Parallel MR TransmissionSlide2

Outline

K-space analysis of small tip-angle excitation

RF shimming and Parallel MR Transmission

B

1

mapping

Accelerated MR excitations

Homogeneity and SAR minimizationSlide3

K-Space Interpretation of Small Tip Angle Excitation

New point of view for analyzing selective excitation

Similar approach as that of data acquisition and reconstruction

Strictly valid only for small tip angles excitations but holds also for flip angles ~ 90°

Bloch equation in the rotating frame

(ignoring T

1

and T

2

)Slide4

Excitation K-Space

(parametrically describes a path through the spatial frequency space)

Parametric description of the unit-weight trajectory (

sampling structure)

Spatial-frequency weighting of the

k

-space trajectorySlide5

Application to Slice-Selective Excitation

Conventional slice-selective excitation pulse sequence

k

-space interpretation

K-space is scanned linearly as the RF field is applied

The location in

k

-space at time

t

is the integral of the remaining gradient waveform

Origin reached when the remaining waveform integrates to zero

RF weighting is symmetric with respect to the origin

Slice profile (Fourier transform of RF weighting) is in phase

The role of the refocusing lobe is to shift the

k

-space origin back in the middle of the RF excitation Slide6

Multiple Coil Excitations

a

1,

φ

1

a

2,

φ

2

a

8,

φ

8

a

7,

φ

7

a

6,

φ

6

a

5,

φ5

a3,

φ3

a4,

φ4

RF

RF

RF

RF

RF

RF

RF

RF

RF

a

2

(t)

,

φ

2

(t)

a

3

(t)

,

φ

3

(t)

a

4

(t)

,

φ

4

(t)

a

1

(t)

,

φ

1

(t)

a

7

(t)

,

φ

7

(

t)

a

6

(t)

,

φ

6

(t)

a

5

(t

)

,

φ

5

(t)

a

8

(t)

,

φ

8

(t)

RF shimming

Distinct but time-constant amplitudes and phases for each element

Common gradient and RF waveform

Parallel Transmission

Distinct and time-varying amplitudes and phases for each element

Common gradient waveform but distinct RF waveformSlide7

Parallel RF Transmission

Parallel transmission may be used to correct RF inhomogeneities, control SAR, tailor excitations

Requires calibration of coil array excitation patterns, and operates in close analogy to parallel receptionSlide8

Small Flip Angle Excitation

Homogeneous volume coil

excitation

k

-space sampling trajectory

(controlled by the switching gradients)

spatial-frequency weighting

(proportional to the coil driving current)

Transmit coil array

(

M

xy

is obtained by multiplying the profile by

iγM

0

)

B

1

spatial

weighting

Question:

what is the B

1

spatial weighting?

Effective spatial weighting, to account for coupling-induced

intercoil

correlationsSlide9

Illustration of Parallel Transmission

1 RF pulse

+ the gradient pulseSlide10

Illustration of Parallel Transmission

1 RF pulse

+ the gradient pulse

+ B

1

weightingSlide11

Illustration of Parallel Transmission

L (coils) RF pulses

+ the gradient pulse

+ B

1

weightingSlide12

Example: 2D Selective ExcitationSlide13

Example: 3D Selective ExcitationSlide14

Outline

K-space analysis of small tip-angle excitation

RF shimming and Parallel MR Transmission

B

1

mapping

Accelerated MR excitations

Homogeneity and SAR minimizationSlide15

B1

Mapping

Accurate transmit RF field (B

1

+

) or flip angle maps are needed for many MR applications.

Examples?

Correct the results of quantitative methods Validate theoretical models for EM calculations

Testing MR compatibility of implanted objects Compensate for B1 inhomogeneitiesImage-based RF field measurements are needed for in-vivo

applications

Several B

1

mapping techniques exists, but further improvements (time efficiency, anatomical coverage, accuracy) are needed to use them in the routine practice and for parallel transmissionSlide16

Multi-Point Intensity Method

Non-selective RF pulse (long TR) and FID

Signal is largely independent from T

1

and T

2S ∝sin(α)

Step through transmit voltage until the first signal maximum is found (i.e. α = 90°)

Other pulse amplitudes would then be set relative to this calibration pulseFor GRE:Slide17

Double Angle Method (DAM)

Collect two scans, one of which uses twice the RF amplitude of the other.

image value at

pixel

j

object magnetization

at voxel

j

unknown actual

flip angle

error

“Double angle formula”Slide18

Double Angle Method (DAM)

Collect two scans, one of which uses twice the RF amplitude of the other.

image value at

pixel

j

object magnetization

at voxel

j

unknown actual

flip angle

error

Inefficient method (TR

5T

1

required)

Performs poorly in regions of low signal

ambiguities

if

is

too large, sensitive to noise if

is

too small

“Double angle formula”Slide19

Phase-Based Method

Exploits the fact that rotations do not commute

Final M

xy

differs by a phase

that depends on the magnitude of the

flip angle

α

α

x

α

y

α

-

x

α

-

y

α

x

α

y

α

y

α

x

α

-

y

α

-

x

α

y

α

xSlide20

Question:

What are pros and cons of the phase-based method?Slide21

Phase-Based Method

Exploits the fact that rotations do not commute

Final M

xy

differs by a phase

that depends on the magnitude of the

flip angle

α

Works

better for larger

α

and shorter pulses

(

SAR limitation)

Only for 3D and sensitive to motion/flow

α

x

α

y

α

-

x

α

-

y

α

x

α

y

α

y

α

x

α

-

y

α

-

x

α

y

α

xSlide22

Actual Flip Angle Imaging (AFI)

T

wo identical RF pulses followed by two delays of different

duration (TR

1

< TR

2

< T

1

)

Assumption: at the end of both TR

1

and TR

2

the transverse magnetization is completely spoiled (need RF spoiling with dummy repetition to reach steady state)

Before each excitation pulse:

The observed signals are:

Their ratio is:Slide23

Any questions?Slide24

Outline

K-space analysis of small tip-angle excitation

RF shimming and Parallel MR Transmission

B

1

mapping

Accelerated MR excitations

Homogeneity and SAR minimizationSlide25

Parallel Transmit For 2D EPI Excitation

Complex-valued excitation profile

Periodic excitation pattern associated with the RF pulse of the

l

th

transmit coil

In the case of a 2D EPI excitation trajectory, let’s define:

If the sampling interval in excitation

k

-space is sufficiently small, then

Δx

= 1/Δ

k

x

is big enough that all the aliasing lobes are outside the FOV:

If we

undersample

(i.e. use a larger sampling interval) in excitation

k

-space, then

M

lobes will alias inside the FOV:Slide26

Accelerated Parallel MR Excitations

(in the case of the EPI excitation trajectory we can treat each position separately)

To design our parallel transmit pulse design we need to find the periodic excitation patterns for each transmit coil such that:

Question:

how would the equation above change for an accelerated RF excitation? Slide27

Accelerated Parallel MR Excitations

(in the case of the EPI excitation trajectory we can treat each position separately)

To design our parallel transmit pulse design we need to find the periodic excitation patterns for each transmit coil such that:

We can exploit the extra degrees of freedom to under sample the excitation by a factor

M

: Slide28

Outline

K-space analysis of small tip-angle excitation

RF shimming and Parallel MR Transmission

B

1

mapping

Accelerated MR excitations

Homogeneity and SAR minimizationSlide29

SAR and RF Homogeneity

SAR management and RF homogeneity are critical issues at high magnetic field strengths

SAR is a potentially elevated

safety concern

B

1

focusing compromises

the underlying SNR increaseSlide30

RF Power Deposition

in Multiple Coil Excitations

electric field covariance matrix

RF energy dissipated in

noise covariance matrix

Net Electric Field

EPI excitation trajectory

Small tip angle

Global SAR

Image-domain global SAR

unit current electric field

RF excitation patternsSlide31

Pulse Design for SAR Reduction

weighting

Homogeneous excitation

with minimum SAR

target excitation

profile at

Minimum global SAR

Optimal excitation patterns

for Parallel Transmission

Time-independent RF shimming

Optimal modulation coefficients

shared excitation profile

optimal modulation Slide32

Minimum SAR with Parallel

Tx

SAR =

3.3

20 coils

SAR =

5.5

12 coils

SAR =

7.9

8 coils

Parallel Transmission - 7 Tesla - No Acceleration

SAR =

1

Ultimate

Basis SetSlide33

SAR vs. Profile Homogeneity

B

o

= 7TSlide34

Calibrating the Phi Matrix

2

3

4

1

3

4

1

2Slide35

Calibrating the Phi Matrix

2

4

1

3

3

1

2

4Slide36

Calibrating the Phi Matrix

4

1

3

2

3

4

1

2Slide37

How Many Measurements?

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Experiment

Channel

1

2

3

4

4 real

diagonal elements

6

complex

off-diagonal elements

16 variables to estimate

16 (# of channels × # of channels) measurements required

Question:

Why 16 measurements?Slide38

Simulation Results

1

2

3

4

Φ

calibrated using

simulated E fields

Φ

calibrated using

power measurements

Identical !

Measured and predicted power

Simulation set upSlide39

Experimental Set Up (7 Tesla)

Directional couplers

RF switch

National Instrument Dual 16x1 MUX

Knee setup,

8-channel parallel

Tx

stripline

coil

Power meter

Rhodes & Schwarz

NRP

-Z11

Computer that automates the measurementSlide40

In-Vivo Results

40-miliseconds

Φ

calibrated at 60V

40-miliseconds

Φ

calibrated

at

120V

measured

power

predicted

powerSlide41

Uses of Phi Matrix Calibration

Prediction and real-time monitoring of global SAR

Prediction and real-time monitoring of individual channel FWD and RFL power

Real-time detection of

Tx

chain hardware failures

Optimization of RF pulse design for RF shimming and parallel transmissionSlide42

Maximum Efficiency RF Shimming

Array transmit efficiency metric:

Average B

1

+

strength squared:

Total power deposition

# of spatial locations

It can be treated as a generalized

eigenvalue

problem:

Largest

eigenvalue

= maximum transmit efficiency

η

max

Corresponding eigenvector =

w

max

for maximum efficiency RF shimming

Maximum Efficiency RF Shimming

Find

w

that maximize

ηSlide43

Experiment: Hip Imaging at 7 T

Flip Angle Maps

90

0

π

Excitation: 4

ch

Tx

/Rx loop coils

Receive: 10

ch

Tx

/Rx

(5 loop/

stripline

modules)

Conservative parallel transmit SAR limits were used

Φ

matrix computed from forward and reflected power measures

RF Shim weights

Γ

- matrix

No Shimming

Φ

- matrixSlide44

RF Shimming Weights Calculation

B

1

+

map acquisition and field extraction: ~1 min

Φ

matrix calibration:

< 5 seconds

Maximum

efficiency weights calculation

: < 1

sSlide45

Results: RF Shimming at 7 T

No RF Shimming

Maximum Efficiency RF Shimming

Transmit Efficiency (

η

)

117

286

Measured Total Average Energy Deposition (Watts)

155

58.8

Mean Flip angle in ROI

28.8° ± 10.7°

25.1° ± 10.9°Slide46

Any questions?Slide47

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