1. G Practical MRI 1
Receive Arrays

2. Receive Arrays Are Critical in MRI
Advantages
SNR
Speed (parallel MRI)
Volumetric coverage
Image quality
Simplicity
Disadvantages
Cost
Complexity
Data load …
How many elements do we need?

3. 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!

4. SNR at Depth more coils are better up to a certain point ! SNR
Body noise
dominated
Coil noise
dominated
SNR
Number of elements
more coils are better up to a certain point !

5. 128-Element Cardiac Array
Front Back

6. 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?

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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)

13. 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

14. Active Detuning Schematic
DC + RF

15. 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 times)
The industry standard preamplifier has noise figure less than 0.5 dB

16. 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
For applications such as fMRI is critical that the complex gain remains stable (over at least 5 minutes)

17. Power Matching
The goal is maximum power extraction from signal source (i.e. no reflected power)
Maximum power for

18. Noise Matching
The goal is maximum signal-to-noise ratio (SNR) at the preamp output
equivalent noise sources
Ideal noise-free preamp

19. Noise Factor and Other Quantities
S = signal power
N = noise power
“Noise Factor”
en = input referred spectral noise voltage density [V ·Hz-1/2]
in = input referred spectral noise current density [A ·Hz-1/2]
= thermal noise voltage density of source resistor [V ·Hz-1/2]
noise input resistance of the preamplifiers in Ohms
spectral noise power density of the preamplifiers in W/Hz

20. Noise Matching Condition
For a bandwidth Δf (assuming no correlation between en and in:
minimum noise factor for

21. Noise Figure vs. ρn for power matching was noise matching for:
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
for power matching was
noise matching for:

22. 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

23. Equivalent Circuit For Coupling
resistive coupling
capacitive coupling
inductive coupling

24. 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
“magnetic coupling coefficient”

25. 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

26. 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:
“mutual resistance”

27. 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?

28. 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

29. 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

30. Coil Overlapping in Parallel Imaging
Baseline SNR and g-factor are empirically optimized
for target image planes and accelerations
Intrinsic Noise
g-factor
Final Noise

31. Geometric Decoupling Example
w ~ 1 / (LC)1/2
single surface
coil

32. Geometric Decoupling Example
lightly coupled
coils

33. Geometric Decoupling Example
strongly coupled
coils

34. Geometric Decoupling Example
critical overlap

35. Geometric Decoupling Example
Single Coil
Lightly Coupled
Strongly Coupled
Critical Overlap

36. Preamplifier Decoupling
It has been the enabling technology for many-element receive arrays
It prevents currents from flowing around the coil, so signal cannot couple inductively
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

37. 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
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

38. 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
ANSWER: we need current flowing around the coil for transmission

39. 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

40. 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

41. 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)

42. 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

43. 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

44. Any questions?

45. Acknowledgments
The slides relative to the geometric decoupling example are courtesy of Dr. Graham Wiggins

46. See you next week!