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G16.4427 Practical MRI 1
Receive Arrays
G16.4427 Practical MRI 1 – 9th April 2015
Receive Arrays Are Critical in MRI
• Advantages
• Disadvantages
– SNR
– Cost
– Speed (parallel MRI)
– Complexity
– Volumetric coverage
– Data load
– Image quality
–…
– Simplicity
How many elements do we need?
G16.4427 Practical MRI 1 – 9th April 2015
Benefits for Parallel Imaging
• Max acceleration = # of detector coils
– Need more coils to go faster!
• Intrinsic SNR loss
– Need more coils for multi-dimensional
acceleration and volumetric coverage!
• Noise amplifications (geometry factor)
– Need more coils for improved encoding
capabilities!
G16.4427 Practical MRI 1 – 9th April 2015
SNR at Depth
SNR
Body noise
dominated
Coil noise
dominated
Number of elements
more coils are better up to a certain point !
G16.4427 Practical MRI 1 – 9th April 2015
128-Element Cardiac Array
Front
Back
G16.4427 Practical MRI 1 – 9th April 2015
Coil Design Challenges
• What is the minimum practical coil size?
• What is the optimal number of elements?
• What is the best geometrical arrangement?
• How do we decouple the elements?
• What is the best cable layout?
G16.4427 Practical MRI 1 – 9th April 2015
Do not get scared: each element of a coil
array is a surface coil designed to receive
the signal from the nuclear spins
Let’s start by reviewing some principles
of receive-only surface coil design
G16.4427 Practical MRI 1 – 9th April 2015
Transmit Detuning
• During RF excitation, receive coils must be
transparent so B1+ is not distorted
– Limiting the currents on the coil induced by the
transmit field to negligible levels by ensuring that
the total impedance of the coil loop is very high
G16.4427 Practical MRI 1 – 9th April 2015
Transmit Detuning
• During RF excitation, receive coils must be
transparent so B1+ is not distorted
– Limiting the currents on the coil induced by the
transmit field to negligible levels by ensuring that
the total impedance of the coil loop is very high
• Total coil impedance must be switched from
low during receive to high during transmission
– Passive detuning
– Active detuning
G16.4427 Practical MRI 1 – 9th April 2015
Passive Detuning
• Use a pair of crossed high-speed diodes
– Diodes act as a switch that connects a parallel
resonant trap to the coil thus opening the circuit
Surface Loop Coil
G16.4427 Practical MRI 1 – 9th April 2015
Passive Detuning
• Use a pair of crossed high-speed diodes
– Diodes act as a switch that connects a parallel
resonant trap to the coil thus opening the circuit
High-Z Trap
G16.4427 Practical MRI 1 – 9th April 2015
Passive Detuning
• Use a pair of crossed high-speed diodes
– Diodes act as a switch that connects a parallel
resonant trap to the coil thus opening the circuit
• Used mostly as redundant safety feature
– If the transmit field not strong enough diodes will
not be fully switched
– Passive traps cannot be monitored independently
to identify potentially dangerous situations (e.g.
diodes burn out)
G16.4427 Practical MRI 1 – 9th April 2015
Active Detuning
• Required bringing an external DC bias voltage
to diodes on the coil
– The additional logic signal required to switch the
coil between transmit and receive states is
supplied either on a dedicated line or using the RF
power amplifier’s un-blank signal
– The switching devices most often used today are
PIN diodes, which can control large RF currents
with a small DC current and low RF resistance
G16.4427 Practical MRI 1 – 9th April 2015
Active Detuning Schematic
DC + RF
G16.4427 Practical MRI 1 – 9th April 2015
Preamplifiers
• One of the key hardware elements in an RF coil
from a standpoint of SNR performance
• The induced voltage (i.e. signal) in a coil is very
small, typically on the order of a few μV
• This small signal is amplified to a few mV by a
preamplifier with gain ~30 dB (i.e. 1000 times)
• The industry standard preamplifier has noise
figure less than 0.5 dB
G16.4427 Practical MRI 1 – 9th April 2015
Requirements for MR Applications
• Static magnetic field compatibility
– Preamps are in an extremely strong and homogeneous
static magnetic field
– No ferrites or iron, Cu-only coaxial cables, no magnetic
distortion of B0
• RF and gradient field compatibility
– Ground plane as small and thin as possible to avoid
shielding effects and eddy currents
• Very high dynamic range
– Must work with very small to large input signals
• Accurate complex gain reproducibility
• Aid in decoupling of resonant loops in array
• Must be protected against transmit power and
excessive heating
G16.4427 Practical MRI 1 – 9th April 2015
Power Matching
• The goal is maximum power extraction from
signal source (i.e. no reflected power)
rs
iin
vs
v
Ps =
rs
vin
vin2
rs rin
Pin =
= Ps ×
rin
rs + rin
(
rin
)
rin
rin =
rs
Pin ( rin ) = Ps ×
2
s
(r
rin
in
)
+1
2
Maximum power for rin = 1
G16.4427 Practical MRI 1 – 9th April 2015
2
Noise Matching
• The goal is maximum signal-to-noise ratio (SNR)
at the preamp output
equivalent noise sources
er
en
rs
vs
in
SNRin
Ideal noise-free preamp
G16.4427 Practical MRI 1 – 9th April 2015
SNRout
Noise Factor and Other Quantities
Sin / N in
F=
Sout / N out
“Noise Factor”
S = signal power
N = noise power
en = input referred spectral noise voltage density [V ·Hz-1/2]
in = input referred spectral noise current density [A ·Hz-1/2]
er = 4k BTrs = thermal noise voltage density of source resistor [V ·Hz-1/2]
en
rn =
in
noise input resistance of the preamplifiers in Ohms
pn = en × in spectral noise power density of the preamplifiers in W/Hz
G16.4427 Practical MRI 1 – 9th April 2015
Noise Matching Condition
For a bandwidth Δf (assuming no correlation between en and in:
Sin
Ps
Ps
SNRin =
= 2
=
N in er Df / rs 4k BT Df
SNRout =
Sout
P
= 2 2 2s 2
N out (er + en + in rs )(Df / rs )
2
SNRin er2 + en2 + in2 rs2
1 æ en 2 ö
F=
=
= 1+
+ in rs ÷
ç
SNRout
4k BTrs
4k BT è rs
ø
rn pn = en2
pn
= in2
rn
rn
rn º
rs
F( r n , pn ) = 1+
(
pn
r n + r n-1
4k BT
)
minimum noise factor for r n,opt = 1
G16.4427 Practical MRI 1 – 9th April 2015
rs = rn
Noise Figure vs. ρn
If we have a good
transistor with a small pn,
even if we do not meet
exactly the minimum, the
noise figure is still ~Fmin
the smaller the noise
figure of a preamp (i.e. the
smaller pn), the wider the
allowed range of source
impedance rs
(
pn
F( r n , pn ) = 1+
r n + r n-1
4k BT
)
for power matching was P( rin ) = P( rin-1 )
noise matching for: F( rn ) = F( rn-1 )
pn
Fmin ( pn ) = 1+
2k BT
G16.4427 Practical MRI 1 – 9th April 2015
Array Coupling
• Creating an array is not as simple as putting
together a number of surface coil elements
– Coupling reduces the spatial uniqueness of the
signal acquired from the coils due to signal
crosstalk and introduces correlation in the noise
between channels
• Electromagnetically, coupling can be divided
into three categories based on the fields that
it originates from
G16.4427 Practical MRI 1 – 9th April 2015
Equivalent Circuit For Coupling
capacitive coupling
resistive coupling
inductive coupling
G16.4427 Practical MRI 1 – 9th April 2015
Inductive Coupling
• Due to the direct
interaction of coil loops
through magnetic fields
produced by currents that
are flowing on the
conductors
• The equivalent circuit is a
mutual inductance (M), or
transformer, and leads to
changes in the frequency
response of the elements
and degrade their
sensitivity
km =
M
L1 L2
km Î éë -1,1ùû
“magnetic coupling coefficient”
G16.4427 Practical MRI 1 – 9th April 2015
Electric (Capacitive) Coupling
• Electric coupling is due to the direct interaction of
coil loops through (conservative) electric fields
due to charges on the coils (Coulomb fields),
which is equivalent to a mutual capacitance
between the coils
• This parasitic capacitance is more relevant at
higher frequencies (smaller reactance) and can be
enhanced by body/phantom permittivity,
therefore making it sensitive to positioning,
patient size, etc.
• It can also be introduced or controlled to
compensate for inductive coupling
G16.4427 Practical MRI 1 – 9th April 2015
Resistive Coupling
• Due to the indirect interaction of coil loops
through currents supported by the finite
conductivity of the body or phantom on which
the array is placed
• Appears as a mutual resistance term in the
equivalent circuit:
R12 =
ò
s (r)E1 (r) ×E (r)dv
*
2
ke12 =
sample
“mutual resistance”
G16.4427 Practical MRI 1 – 9th April 2015
R12
R1 R2
Mutual Resistance
• Determines the lowest achievable coupling
(i.e. by eliminating the reactive components)
• Cannot be eliminated by any decoupling
method
• Is associated with intrinsic noise correlation
that influences image reconstruction and SNR
• Question: in what conditions it is zero?
G16.4427 Practical MRI 1 – 9th April 2015
Mutual Resistance
• Determines the lowest achievable coupling
(i.e. by eliminating the reactive components)
• Cannot be eliminated by any decoupling
method
• Is associated with intrinsic noise correlation
that influences image reconstruction and SNR
• Is zero in lossless media
• Some geometrical coil configurations can be
found where resistive coupling is zero
G16.4427 Practical MRI 1 – 9th April 2015
Geometric Decoupling
• Standard method between nearest neighbors
• Coil overlapped at a distance for which mutual
inductance become zero
– Only parasitic capacitance and mutual resistance
• Has the advantage of being broadband
• There are some limitations:
– Cannot be extended beyond three coils or between
non-neighboring coils
– Non optimal for parallel imaging spatial encoding
– Increase noise correlation
G16.4427 Practical MRI 1 – 9th April 2015
Coil Overlapping in Parallel Imaging
• Baseline SNR and g-factor are empirically optimized
for target image planes and accelerations
Intrinsic Noise
g-factor
G16.4427 Practical MRI 1 – 9th April 2015
Final Noise
Geometric Decoupling Example
w ~ 1 / (LC)1/2
single surface
coil
G16.4427 Practical MRI 1 – 9th April 2015
Geometric Decoupling Example
lightly coupled
coils
G16.4427 Practical MRI 1 – 9th April 2015
Geometric Decoupling Example
strongly coupled
coils
G16.4427 Practical MRI 1 – 9th April 2015
Geometric Decoupling Example
critical overlap
G16.4427 Practical MRI 1 – 9th April 2015
Geometric Decoupling Example
Single Coil
Lightly Coupled
Strongly Coupled
G16.4427 Practical MRI 1 – 9th April 2015
Critical Overlap
Preamplifier Decoupling
• It has been the enabling technology for manyelement receive arrays
• It prevents currents from flowing around the
coil, so signal cannot couple inductively
Vout = Vsignal
æ
æ
1 öö
+ ç R1 + i ç w L1 I1
÷
÷
w C1 ø ø
è
è
+iw M12 I 2
By tuning and matching we minimize the
noise associated with coil 1
With geometric decoupling we set M12 = 0,
with preamp decoupling we set I2 = 0
G16.4427 Practical MRI 1 – 9th April 2015
Three Design Goals
Step-up network (series resonance) that
create a short-equivalent and impedance
transformation to achieve 50 Ω match
First transistor of the preamp with
equivalent noise input resistance rn
C1
L1
The coil must
see almost a
short: rn ≈ 5 Ω
The preamp must
see a 50 Ω source:
R0 = 50 Ω
The preamp must
be noise matched:
rs = rn ≈ 1 kΩ
G16.4427 Practical MRI 1 – 9th April 2015
Reactive Decoupling
• If the coupling matrix is known it is possible to
design networks of capacitors and inductors
that introduce couplings that are equal but
opposite to those present between the coils
• Used in Tx/Rx arrays where preamp decoupling
is not feasible. Question: why?
• Limitations:
– Changes is coupling with time, position, loading are
not easily accommodated
– generally a narrowband technique
G16.4427 Practical MRI 1 – 9th April 2015
Reactive Decoupling
• If the coupling matrix is known it is possible to
design networks of capacitors and inductors
that introduce couplings that are equal but
opposite to those present between the coils
• Used in Tx/Rx arrays where preamp decoupling
is not feasible. Question: why?
• Limitations:
– Changes is coupling with time, position, loading are
not easily accommodated
– generally a narrowband technique
G16.4427 Practical MRI 1 – 9th April 2015
Noise Correlation Measurements
• Measurement of noise correlation is required
for optimal-SNR image combination and is also
a commonly used measure of coil coupling
• It is performed by:
– acquiring a sufficient number of noise samples with
the array connected to the MR system and no RF
– Calculating the correlation between data in
different channels
– We’ll see more in lecture 15
G16.4427 Practical MRI 1 – 9th April 2015
Cabling and Safety Issues
• Cabling and related grounding are critical parts of
any array
• Poor cabling can create:
– additional coupling between channels
– B1+ distortions
– Heating hazards due to currents flowing on ground
conductors during transmission
• Proper cable routing is the first step to avoid these
problems (e.g. route cables along regions of low
electric fields)
G16.4427 Practical MRI 1 – 9th April 2015
Cabling and Safety Issues
• Cabling and related grounding are critical parts of
any array
• Poor cabling can create:
– additional coupling between channels
– B1+ distortions
– Heating hazards due to currents flowing on ground
conductors during transmission
• Proper cable routing is the first step to avoid these
problems (e.g. route cables along regions of low
electric fields)
• Cable traps near the coils and/or baluns along
cables are used to block shield currents that would
flow outside of the shields of the coaxial cables
G16.4427 Practical MRI 1 – 9th April 2015
Essential Principles of Array Design
• Coil arrays designed for parallel MRI need:
– Good baseline SNR
– Effective encoding capabilities
• General requirements apply:
– Decoupling of signal and noise between elements
– Good match circuitry
– Good preamplifiers behavior
• Spatial encoding capabilities are controlled by
tailoring the shape and distribution of coil
sensitivities to maximize feasible acceleration
G16.4427 Practical MRI 1 – 9th April 2015
Any questions?
G16.4427 Practical MRI 1 – 9th April 2015
Acknowledgments
• The slides relative to the geometric
decoupling example are courtesy of Dr.
Graham Wiggins
G16.4427 Practical MRI 1 – 9th April 2015
See you next week!
G16.4427 Practical MRI 1 – 9th April 2015