G16.4427 Practical MRI 1 – 2nd April 2015
G16.4427 Practical MRI 1
Volume and Surface Coils
G16.4427 Practical MRI 1 – 2nd April 2015
MR Coils• An MR coil is an inductor capable of producing
and/or detecting a time-varying magnetic field– It can be represented as an inductance L, with a
series resistance RL, driven by an alternating current source (in Tx) or by the received MR signal
“Circuit forAC-drive realistic
inductor”
G16.4427 Practical MRI 1 – 2nd April 2015
Coil Impedance• When a voltage is applied, the current will be
inversely proportional to the impedance– In Tx, power must be delivered efficiently to the
inductor with minimum current at given impedance– In Rx, the induced current must encounter minimum
resistance in the MR inductor circuit– For optimum performance the impedance is minimized
and matches the Tx/Rx (source) system impedance
G16.4427 Practical MRI 1 – 2nd April 2015
Coil Impedance• When a voltage is applied, the current will be inversely
proportional to the impedance– In Tx, power must be delivered efficiently to the inductor
with minimum current at given impedance– In Rx, the induced current must encounter minimum
resistance in the MR inductor circuit– For optimum performance the impedance is minimized and
matches the Tx/Rx (source) system impedance• The coil impedance can be expressed as:– Zcoil = ZL = RL + iXL = RL + iωL
– Typically a receive coil will have RL ~ 1 Ω and variable inductance depending on size and configuration
G16.4427 Practical MRI 1 – 2nd April 2015
Tuned Circuits• The inductor circuit need to operate efficiently
at the MR frequency of the spin of interest– Tune the circuit with a capacitive-reactive element
to provide the appropriate impedance
“Series tuning” “Parallel tuning”
G16.4427 Practical MRI 1 – 2nd April 2015
Problem
Given: • RL = 0.320 Ω• L = 0.110 μHFind the value of the series capacitor that will make the circuit to resonate at the proton resonance frequency at 3 Tesla
G16.4427 Practical MRI 1 – 2nd April 2015
Parallel-Tune Coil• Has a resistive impedance at resonance that
depends on the value of C and L– Can be used to transform the circuit resistance
Parallel tuning effectively transforms the resistance of the circuit
G16.4427 Practical MRI 1 – 2nd April 2015
Impedance Matching• The coil circuit must have the impedance matched to the Tx/Rx
(source) impedance– However, the series resistance of an MR coil is ~ 1 Ω, much less than the
typical source impedance of 50 Ω• A combination of series- and parallel-tuned circuit is used to allow
both resonance and impedance matching
G16.4427 Practical MRI 1 – 2nd April 2015
Impedance Matching• The coil circuit must have the impedance matched to the Tx/Rx
(source) impedance– However, the series resistance of an MR coil is ~ 1 Ω, much less than the
typical source impedance of 50 Ω• A combination of series- and parallel-tuned circuit is used to allow
both resonance and impedance matching
G16.4427 Practical MRI 1 – 2nd April 2015
Expression for the ImpedanceUsing the series-equivalent representation:
Substituting:must be zero (2 valid solutions)
must be equal to 50 ΩThe desired frequency response can be determined by requiring that the impedance be pure resistive and equal to the source impedance at the frequency of interest
G16.4427 Practical MRI 1 – 2nd April 2015
ExampleLet’s look at the simulated performance of a surface coil modeled with the circuit we saw, tuned at 200 MHz and matched at 50 Ω
G16.4427 Practical MRI 1 – 2nd April 2015
ExampleLet’s look at the simulated performance of a surface coil modeled with the circuit we saw, tuned at 200 MHz and matched at 50 Ω
Real part of the impedance (resistance)
Imaginary part of the impedance (reactance)
Note that the reactance has two zeros (200 MHz and 205 MHz) and the lower frequency represents the appropriate one because it corresponds to a resistance of 50 Ω
G16.4427 Practical MRI 1 – 2nd April 2015
Circular Loop Coil
The field from the circular loop can be found from Biot-Savart law:
In the case of thin wires ( J(x) = Idl ):
Haacke et al. (1999) Magnetic Resonance Imaging
G16.4427 Practical MRI 1 – 2nd April 2015
Sensitivity Profile of the Loop CoilAn elementary calculation can be made to find the on-axis field:
Maximum SNR at depth d is obtained with loop of radius:
G16.4427 Practical MRI 1 – 2nd April 2015
Example of Surface Coils
• Receiver system brought closer to patients• Detect noise from a limited volume• Has good SNR for superficial tissues
Surface coils are placed on or around the surface of a patients.Question: what are the advantages of surface coils?
G16.4427 Practical MRI 1 – 2nd April 2015
Whole-Volume Coils
• Can be used for surrounding either the whole body or a specific region
• Allow imaging bigger volumes
• Have better magnetic field homogeneity than surface coils
G16.4427 Practical MRI 1 – 2nd April 2015
Helmholtz Coils• An initial step to produce a magnetic field that
is more homogeneous than that shown for the single loop is two combine two coaxial loops and find the ration of their separation to radii which gives optimal field homogeneity
The optimal arrangement is found by doing a Taylor expansion of the field along the z axis and eliminate the second-order derivative, which yields: a = 2s
Haacke et al. (1999) Magnetic Resonance Imaging
G16.4427 Practical MRI 1 – 2nd April 2015
Magnetic Field for an Helmholtz Coil
G16.4427 Practical MRI 1 – 2nd April 2015
Problem
German physician and physicist
31st August 1821 - 8th September 1894
Hermann von Helmholtz
z = 0
Using the following expression, derived with the Biot-Savart law, for the Bz of each coil, compute the value of B at the mid point between the two coils
G16.4427 Practical MRI 1 – 2nd April 2015
Maxwell Coils• A variation of the Helmholtz coil for improved
field homogeneity (at the expenses of more material and complexity)
Haacke et al. (1999) Magnetic Resonance Imaging
G16.4427 Practical MRI 1 – 2nd April 2015
Classic Solenoid• A solenoid is a coil wound
into a tightly packed helix• From Ampere’s law:
number of turns current
length of solenoid
G16.4427 Practical MRI 1 – 2nd April 2015
Solenoid Uniformity for Body Coil• A classic uniformly wound solenoid is not the
best choice for an MRI main magnet– Good uniformity at the center requires its length to
be large compared to its radius
For Bz to be constant near the origin, then α1 and α2 need to be approximately constant length much greater than radius
Haacke et al. (1999) Magnetic Resonance Imaging
G16.4427 Practical MRI 1 – 2nd April 2015
Birdcage Coils• One of the most popular coil configuration– Quadrature design– Excellent radial field homogeneity over the
imaging volume
• The axial current paths are referred to as the legs• The azimuthal paths are referred to as the endrings
Haacke et al. (1999) Magnetic Resonance Imaging
G16.4427 Practical MRI 1 – 2nd April 2015
Field in a Birdcage Coil• If the current in the legs if the coil is of the
form:
then the field produced in the imaging region is extremely uniform and rotates its direction with angular frequency ω
• Nearly all of the fields produced are used for imaging– The birdcage coil is very efficient
G16.4427 Practical MRI 1 – 2nd April 2015
Birdcage Coil Circuit Analysis
• Each conductor is modeled as an inductance and a resistance• An N leg birdcage has N/2 + 2 resonant modes- Using Kirchhoff law we can find all the resonant frequency and
calculate the corresponding magnetic field
G16.4427 Practical MRI 1 – 2nd April 2015
Different Types of Birdcage Coils
Low Pass Birdcage High Pass Birdcage Hybrid Birdcage
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Examples of Birdcage Coils
High Pass Birdcage Hybrid Birdcage
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Uniform Mode
The magnetic flux lines inside and outside acylindrical shell carryinga z-directed surface currentwith sin(ϕ) variation
ϕ
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Birdcage Modes
Uniform Mode: I = I0sin(ϕ)
Unwrap
ϕ
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Birdcage ModesUniform Mode: I = I0sin(ϕ)
Unwrap
ϕ
Gradient Mode: I = I0sin(2ϕ)
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B1 Distribution (Oil Phantom)
Uniform Mode Gradient Mode
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Birdcage Coil: Linear Drive
0° Port
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Birdcage Coil: Linear Drive
90° Port
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Birdcage Coil: Quadrature Drive
0° Port90° Port
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Limitations of the Birdcage Coil• For a finite birdcage the field uniformity
decay axially• The currents in the endrings do not produce
uniform fields within the imaging volume– If the coil’s length is approximately equal to its
diameter, then the coil has good homogeneity over a spherical volume
• The current has to flow all the way around the coil (through the endrings) making the inductance of the circuit very high
G16.4427 Practical MRI 1 – 2nd April 2015
TEM Coil• The TEM coil is a cavity
resonator– A space bounded by an electrically
conducting surface and in which oscillating electromagnetic energy is stored
• The significant current return path is on the cavity wall, in the z direction– There are no endrings
• Size scaling of TEM coils is easy• Better sensitivity than birdcage
G16.4427 Practical MRI 1 – 2nd April 2015
Birdcage vs. TEM
Shielded LP Birdcage TEM Coil
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Current Paths
Shielded LP Birdcage TEM Coil
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Ideal Current Patterns at Low Field
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Ideal Current Patterns at 1.5 Tesla• Ideal current patterns appear to
form two distributed loops separated by 180 degrees, which precess at the Larmor frequency around the axis of the cylinder.
• The amplitude of current varies sinusoidally in the azimuthal direction, completing one full cycle around the circumference
• Resemblance with a birdcage coil (with smooth distributed currents and narrower along z)
G16.4427 Practical MRI 1 – 2nd April 2015
Ideal Current Patterns at 7 Tesla
• Ideal current patterns become more complex and the circumferentially-directed portions near the edges of the axial FOV, which at 1.5 T resemble end-ring return currents, seem to disappear
• Possible resemblance with a TEM coil
G16.4427 Practical MRI 1 – 2nd April 2015
TEM Resonator at 8 Tesla
Linear-element TEM volume coil
FDTD calculatedpolarization vector
Vaughan JT et al., in Ultra High Field Magnetic Resonance
Imaging, chapter 6 (Springer).
Ibrahim T, in Ultra High Field Magnetic Resonance
Imaging, chapter 7 (Springer).
G16.4427 Practical MRI 1 – 2nd April 2015
Body Imaging at 7 Tesla
Vaughan JT et al., 2009, MRM 61:244-248
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Simulated Body Imaging at 7 TeslaFDTD models of relative B1 magnitude (T/m)
FDTD models of SAR (W/kg)
Vaughan JT et al., 2009, MRM 61:244-248
G16.4427 Practical MRI 1 – 2nd April 2015
Any questions?
G16.4427 Practical MRI 1 – 2nd April 2015
Acknowledgments• The slides describing the birdcage modes and
the comparison between birdcage and TEM coils are courtesy of Dr. Graham Wiggins
G16.4427 Practical MRI 1 – 2nd April 2015
See you next week!