Pulse Design for Parallel MR Transmission. Outline. Kspace analysis of small tipangle excitation. RF shimming and Parallel MR Transmission. B. 1. mapping. Accelerated MR excitations. Homogeneity and SAR minimization. ID: 277431
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G16.4427 Practical MRI 1
Pulse Design for Parallel MR Transmission
Slide2Outline
Kspace analysis of small tipangle excitation
RF shimming and Parallel MR Transmission
B
1
mapping
Accelerated MR excitations
Homogeneity and SAR minimization
Slide3KSpace Interpretation of Small Tip Angle Excitation
New point of view for analyzing selective excitationSimilar approach as that of data acquisition and reconstructionStrictly 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
)
Slide4Excitation KSpace
(parametrically describes a path through the spatial frequency space)
Parametric description of the unitweight trajectory (
sampling structure)
Spatialfrequency weighting of the
k
space trajectory
Slide5Application to SliceSelective Excitation
Conventional sliceselective excitation pulse sequence
k
space interpretation
Kspace 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
Slide6Multiple Coil Excitations
a
1,
φ1
a2, φ2
a8, φ8
a7, φ7
a6, φ6
a5, 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 timeconstant amplitudes and phases for each element
Common gradient and RF waveform
Parallel Transmission
Distinct and timevarying amplitudes and phases for each element
Common gradient waveform but distinct RF waveform
Slide7Parallel RF Transmission
Parallel transmission may be used to correct RF inhomogeneities, control SAR, tailor excitationsRequires calibration of coil array excitation patterns, and operates in close analogy to parallel reception
Slide8Small Flip Angle Excitation
Homogeneous volume coil
excitation
k
space sampling trajectory
(controlled by the switching gradients)
spatialfrequency weighting
(proportional to the coil driving current)
Transmit coil array
(
M
xy
is obtained by multiplying the profile by
iγM
0)
B
1 spatialweighting
Question: what is the B1 spatial weighting?
Effective spatial weighting, to account for couplinginduced
intercoil
correlations
Slide9Illustration of Parallel Transmission
1 RF pulse
+ the gradient pulse
Slide10Illustration of Parallel Transmission
1 RF pulse
+ the gradient pulse
+ B
1
weighting
Slide11Illustration of Parallel Transmission
L (coils) RF pulses
+ the gradient pulse
+ B
1
weighting
Slide12Example: 2D Selective Excitation
Slide13Example: 3D Selective Excitation
Slide14Outline
Kspace analysis of small tipangle excitation
RF shimming and Parallel MR Transmission
B
1
mapping
Accelerated MR excitations
Homogeneity and SAR minimization
Slide15B1 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 B
1
inhomogeneities
Imagebased RF field measurements are needed for
invivo
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 transmission
Slide16MultiPoint Intensity Method
Nonselective RF pulse (long TR) and FIDSignal is largely independent from T1 and T2S ∝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:
Slide17Double 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”
Slide18Double 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”
Slide19PhaseBased Method
Exploits the fact that rotations do not commuteFinal Mxy differs by a phase that depends on the magnitude of the flip angle α
α
x
α
y
α

x
α

y
α
x
αy
αy
αx
αy
αx
αy
αx
Slide20Question:
What are pros and cons of the phasebased method?
Slide21PhaseBased Method
Exploits the fact that rotations do not commuteFinal Mxy 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
αy
αy
αx
αy
αx
αy
αx
Slide22Actual Flip Angle Imaging (AFI)
Two identical RF pulses followed by two delays of different duration (TR1 < TR2 < T1)
Assumption: at the end of both TR1 and TR2 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:
Slide23Any questions?
Slide24Outline
Kspace analysis of small tipangle excitation
RF shimming and Parallel MR Transmission
B
1
mapping
Accelerated MR excitations
Homogeneity and SAR minimization
Slide25Parallel Transmit For 2D EPI Excitation
Complexvalued 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:
Slide26Accelerated 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?
Slide27Accelerated 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
:
Slide28Outline
Kspace analysis of small tipangle excitation
RF shimming and Parallel MR Transmission
B
1
mapping
Accelerated MR excitations
Homogeneity and SAR minimization
Slide29SAR 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 increase
Slide30RF 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
Imagedomain global SAR
unit current electric field
RF excitation patterns
Slide31Pulse Design for SAR Reduction
weighting
Homogeneous excitation
with minimum SAR
target excitation
profile at
Minimum global SAR
Optimal excitation patterns
for Parallel Transmission
Timeindependent RF shimming
Optimal modulation coefficients
shared excitation profile
optimal modulation
Slide32Minimum 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 Set
Slide33SAR vs. Profile Homogeneity
B
o
= 7T
Slide34Calibrating the Phi Matrix
2
3
4
1
3
4
1
2
Slide35Calibrating the Phi Matrix
2
4
1
3
3
1
2
4
Slide36Calibrating the Phi Matrix
4
1
3
2
3
4
1
2
Slide37How 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 elements6 complex offdiagonal elements
16 variables to estimate
16 (# of channels × # of channels) measurements required
Question:
Why 16 measurements?
Slide38Simulation Results
1
2
3
4
Φ
calibrated using
simulated E fields
Φ
calibrated using
power measurements
Identical !
Measured and predicted power
Simulation set up
Slide39Experimental Set Up (7 Tesla)
Directional couplers
RF switch
National Instrument Dual 16x1 MUX
Knee setup,
8channel parallel
Tx
stripline
coil
Power meter
Rhodes & Schwarz
NRP
Z11
Computer that automates the measurement
Slide40InVivo Results
40miliseconds
Φ
calibrated at 60V
40miliseconds
Φ
calibrated
at
120V
measured
power
predicted
power
Slide41Uses of Phi Matrix Calibration
Prediction and realtime monitoring of global SAR
Prediction and realtime monitoring of individual channel FWD and RFL power
Realtime detection of
Tx
chain hardware failures
Optimization of RF pulse design for RF shimming and parallel transmission
Slide42Maximum 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
η
Slide43Experiment: Hip Imaging at 7 T
Flip Angle Maps
90
0
π
π
Excitation: 4
ch
Tx
/Rx loop coils
Receive: 10
ch Tx/Rx (5 loop/stripline modules)Conservative parallel transmit SAR limits were usedΦ matrix computed from forward and reflected power measures
RF Shim weights
Γ
 matrix
No Shimming
Φ
 matrix
Slide44RF Shimming Weights Calculation
B
1+ map acquisition and field extraction: ~1 min
Φ matrix calibration: < 5 seconds
Maximum
efficiency weights calculation
: < 1
s
Slide45Results: RF Shimming at 7 T
No RF Shimming
Maximum Efficiency RF Shimming
Transmit Efficiency (η)117286Measured Total Average Energy Deposition (Watts) 15558.8Mean Flip angle in ROI28.8° ± 10.7°25.1° ± 10.9°
Slide46Any questions?
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