G16.4427 Practical MRI 1 Receive Arrays

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?

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!

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 !

128-Element Cardiac Array Front Back

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?

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

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

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

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

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

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)

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

Active Detuning Schematic DC + RF

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

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)

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

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

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

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

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:

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

Equivalent Circuit For Coupling resistive coupling capacitive coupling inductive coupling

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”

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

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”

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?

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

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

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

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

Geometric Decoupling Example lightly coupled coils

Geometric Decoupling Example strongly coupled coils

Geometric Decoupling Example critical overlap

Geometric Decoupling Example Single Coil Lightly Coupled Strongly Coupled Critical Overlap

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

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

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

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

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

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)

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

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

Any questions?

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

See you next week!