G16.4427 Practical MRI 1 – 2 nd April 2015 G16.4427 Practical MRI 1 Volume and Surface Coils

G16.4427 Practical MRI 1 – 2nd April 2015

G16.4427 Practical MRI 1

Volume and Surface Coils


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”


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


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


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”


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


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


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


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


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


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


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


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


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:


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?


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


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



Magnetic Field for an Helmholtz Coil


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


Maxwell Coils• A variation of the Helmholtz coil for improved

field homogeneity (at the expenses of more material and complexity)



Classic Solenoid• A solenoid is a coil wound

into a tightly packed helix• From Ampere’s law:

number of turns current

length of solenoid


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



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



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


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


Different Types of Birdcage Coils

Low Pass Birdcage High Pass Birdcage Hybrid Birdcage


Examples of Birdcage Coils

High Pass Birdcage Hybrid Birdcage


Uniform Mode

The magnetic flux lines inside and outside acylindrical shell carryinga z-directed surface currentwith sin(ϕ) variation

ϕ


Birdcage Modes

Uniform Mode: I = I0sin(ϕ)

Unwrap

ϕ


Birdcage ModesUniform Mode: I = I0sin(ϕ)

Unwrap

ϕ

Gradient Mode: I = I0sin(2ϕ)


B1 Distribution (Oil Phantom)

Uniform Mode Gradient Mode


Birdcage Coil: Linear Drive

0° Port


Birdcage Coil: Linear Drive

90° Port


Birdcage Coil: Quadrature Drive

0° Port90° Port


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


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


Birdcage vs. TEM

Shielded LP Birdcage TEM Coil


Current Paths

Shielded LP Birdcage TEM Coil


Ideal Current Patterns at Low Field


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)


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


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).


Body Imaging at 7 Tesla

Vaughan JT et al., 2009, MRM 61:244-248


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


Any questions?


Acknowledgments• The slides describing the birdcage modes and

the comparison between birdcage and TEM coils are courtesy of Dr. Graham Wiggins


See you next week!

Documents

G16.4427 Practical MRI 1 – 2 nd April 2015 G16.4427 Practical MRI 1 Volume and Surface Coils