G16.4427 Practical MRI 1 - PowerPoint Presentation

Slide1

G16.4427 Practical MRI 1

Volume and Surface CoilsSlide2

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 for

AC-drive realistic inductor”Slide3

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 impedanceIn Rx, the induced current must encounter minimum resistance in the MR inductor circuitFor optimum performance the impedance is minimized and matches the Tx

/Rx (source) system impedanceSlide4

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 impedanceIn Rx, the induced current must encounter minimum resistance in the MR inductor circuitFor optimum performance the impedance is minimized and matches the Tx/Rx (source) system impedance

The coil impedance can be expressed as:Z

coil = ZL = RL +

iXL

= RL + iωLTypically a receive coil will have

RL ~ 1 Ω and variable inductance depending on size and configurationSlide5

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”Slide6

Problem

Given:

R

L = 0.320 Ω

L = 0.110 μH

Find the value of the series capacitor that will make the circuit to resonate at the proton resonance frequency at 3 TeslaSlide7

Parallel-Tune Coil

Has a resistive impedance at resonance that depends on the value of

C

and LCan be used to transform the circuit resistance

Parallel tuning effectively transforms the resistance of the circuitSlide8

Impedance Matching

The coil circuit must have the impedance matched to the

Tx

/Rx (source) impedanceHowever, the series resistance of an MR coil is ~ 1 Ω, much less than the typical source impedance of 50 ΩA combination of series- and parallel-tuned circuit is used to allow both resonance and impedance matching Slide9

Impedance Matching

The coil circuit must have the impedance matched to the

Tx

/Rx (source) impedanceHowever, the series resistance of an MR coil is ~ 1 Ω, much less than the typical source impedance of 50 ΩA combination of series- and parallel-tuned circuit is used to allow both resonance and impedance matching Slide10

Expression for the Impedance

Using the series-equivalent representation:

Substituting:

must be zero (2 valid solutions)

must be equal to 50

Ω

The desired frequency response can be determined by requiring that the impedance be pure resistive and equal to the source impedance at the frequency of interestSlide11

Example

Let’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

Slide12

Example

Let’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

Slide13

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 ImagingSlide14

Sensitivity Profile of the Loop Coil

An elementary calculation can be made to find the on-axis field:

Maximum SNR at depth

d

is obtained with loop of radius:Slide15

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?Slide16

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 coilsSlide17

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 ImagingSlide18

Magnetic Field for an Helmholtz CoilSlide19

Problem

German physician and physicist

31

st

August 1821 - 8

th

September 1894

Hermann von Helmholtz

z

= 0

Using the following expression,

derived with the

Biot-Savart

law, for the

B

z

of each coil, compute the value of

B at the mid point between the two coils Slide20

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 ImagingSlide21

Classic Solenoid

A solenoid is a coil wound into a tightly packed helix

From Ampere’s law:

number of turns

current

length of

solenoidSlide22

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

B

z

to be constant near the origin, then α

1

and α

2

need to be approximately constant

 length much greater than radius

Haacke et al

. (1999) Magnetic Resonance ImagingSlide23

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 ImagingSlide24

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

ωNearly all of the fields produced are used for imagingThe birdcage coil is very efficientSlide25

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 fieldSlide26

Different Types of Birdcage Coils

Low Pass Birdcage

High Pass Birdcage

Hybrid BirdcageSlide27

Examples of Birdcage Coils

High Pass Birdcage

Hybrid BirdcageSlide28

Uniform Mode

The magnetic flux lines

inside and outside a

cylindrical shell carrying

a

z-directed surface current

with sin(

ϕ) variation

ϕSlide29

Birdcage Modes

Uniform Mode:

I

=

I

0

sin(

ϕ

)

Unwrap

ϕSlide30

Birdcage Modes

Uniform Mode:

I

=

I

0

sin(

ϕ

)

Unwrap

ϕ

Gradient Mode

:

I

=

I

0

sin(

2ϕ

)Slide31

B1 Distribution (Oil Phantom)

Uniform Mode

Gradient ModeSlide32

Birdcage Coil: Linear Drive

0

° PortSlide33

Birdcage Coil: Linear Drive

90

° PortSlide34

Birdcage Coil: Quadrature Drive

0

° Port

90

° PortSlide35

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 volumeIf the coil’s length is approximately equal to its diameter, then the coil has good homogeneity over a spherical volumeThe current has to flow all the way around the coil (through the endrings) making the inductance of the circuit very highSlide36

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 directionThere are no endrings

Size scaling of TEM coils is easyBetter sensitivity than birdcageSlide37

Birdcage vs. TEM

Shielded LP Birdcage

TEM CoilSlide38

Current Paths

Shielded LP Birdcage

TEM CoilSlide39

Ideal Current Patterns at Low FieldSlide40

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

)Slide41

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 coilSlide42

TEM Resonator at 8 Tesla

Linear-element

TEM volume coil

FDTD calculated

polarization 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).Slide43

Body Imaging at 7 Tesla

Vaughan JT et al., 2009, MRM 61:244-248Slide44

Simulated Body Imaging at 7 Tesla

FDTD models of relative B

1

magnitude (T/

m

)

FDTD models of SAR (W/kg)

Vaughan JT et al., 2009, MRM 61:244-248Slide45

Any questions?Slide46

Acknowledgments

The slides

describing the

birdcage modes and the comparison between birdcage and TEM coils are courtesy of Dr. Graham WigginsSlide47

See you next week!